| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2013 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable Force |
| Type | Constant power on horizontal road |
| Difficulty | Standard +0.3 This is a straightforward application of P=Fv and F=ma with constant power. Part (i) requires finding driving force from power equation then applying Newton's second law. Part (ii) requires recognizing that at steady speed, acceleration is zero so driving force equals resistance. Both parts use standard M1 techniques with no conceptual challenges beyond direct formula application. |
| Spec | 3.03c Newton's second law: F=ma one dimension6.02l Power and velocity: P = Fv |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(DF = 1500\ 000/37.5\ (= 40\ 000)\) | B1 | |
| \([DF - R = ma]\) | M1 | For using Newton's second law |
| \(DF - 30\ 000 = 400\ 000a\) | A1 | |
| Acceleration is \(0.025\ ms^{-2}\) | A1 | [4] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \([1500\ 000/v - 30\ 000 = 0]\) | M1 | For using Newton's \(2^{nd}\) law with \(a = 0\) |
| Steady speed is \(50\ ms^{-1}\) | A1 | [2] |
## Question 4:
### Part (i)
| Answer/Working | Mark | Guidance |
|---|---|---|
| $DF = 1500\ 000/37.5\ (= 40\ 000)$ | B1 | |
| $[DF - R = ma]$ | M1 | For using Newton's second law |
| $DF - 30\ 000 = 400\ 000a$ | A1 | |
| Acceleration is $0.025\ ms^{-2}$ | A1 | [4] |
### Part (ii)
| Answer/Working | Mark | Guidance |
|---|---|---|
| $[1500\ 000/v - 30\ 000 = 0]$ | M1 | For using Newton's $2^{nd}$ law with $a = 0$ |
| Steady speed is $50\ ms^{-1}$ | A1 | [2] |
---4 A train of mass 400000 kg is moving on a straight horizontal track. The power of the engine is constant and equal to 1500 kW and the resistance to the train's motion is 30000 N . Find\\
(i) the acceleration of the train when its speed is $37.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }$,\\
(ii) the steady speed at which the train can move.
\hfill \mbox{\textit{CAIE M1 2013 Q4 [6]}}